Now the National Trust, which owns Blickling Hall and park, is renewing its plea for visitors to keep their pets on a lead.

The vicious incident happened about three weeks ago, according to Jo Bosch, marketing and visitor manager at Blickling.

The dogs included a lurcher and possibly all belonged to one person.

“The deer wasn’t killed outright,” said Ms Bosch. “Other visitors were coming across it after it was badly wounded, which was very distressing.”

The animal had been humanely put down to end its suffering, she added.

We are getting a worrying number of people who seem to be ignorant of the fact that we ask for dogs to be kept on leads.”

Lambing season was fast approaching and an out-of-control dog among pregnant ewes or newborn lambs could be disastrous. Loose dogs could also upset cattle, and a number of horse riders had complained that straying dogs were causing a nuisance.

Ms Bosch said: “We’re not trying to be awkward, or ‘jobsworths’, it’s because it’s really important for our tenant farmers, and for other users.”